
theorem
  2837 is prime
proof
  now
    2837 = 2*1418 + 1; hence not 2 divides 2837 by NAT_4:9;
    2837 = 3*945 + 2; hence not 3 divides 2837 by NAT_4:9;
    2837 = 5*567 + 2; hence not 5 divides 2837 by NAT_4:9;
    2837 = 7*405 + 2; hence not 7 divides 2837 by NAT_4:9;
    2837 = 11*257 + 10; hence not 11 divides 2837 by NAT_4:9;
    2837 = 13*218 + 3; hence not 13 divides 2837 by NAT_4:9;
    2837 = 17*166 + 15; hence not 17 divides 2837 by NAT_4:9;
    2837 = 19*149 + 6; hence not 19 divides 2837 by NAT_4:9;
    2837 = 23*123 + 8; hence not 23 divides 2837 by NAT_4:9;
    2837 = 29*97 + 24; hence not 29 divides 2837 by NAT_4:9;
    2837 = 31*91 + 16; hence not 31 divides 2837 by NAT_4:9;
    2837 = 37*76 + 25; hence not 37 divides 2837 by NAT_4:9;
    2837 = 41*69 + 8; hence not 41 divides 2837 by NAT_4:9;
    2837 = 43*65 + 42; hence not 43 divides 2837 by NAT_4:9;
    2837 = 47*60 + 17; hence not 47 divides 2837 by NAT_4:9;
    2837 = 53*53 + 28; hence not 53 divides 2837 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2837 & n is prime
  holds not n divides 2837 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
